{
 "metadata": {
  "name": "",
  "signature": "sha256:59072116e5da289ba149f86ffb2c2aee423cba1b67209b0c0c681ae5cbc8123a"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%matplotlib inline"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# vector addition pt a = (a0,a1), pt b = (b0,b1)\n",
      "a0,b0 = .5,.1\n",
      "a1,b1=rand(2,1000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx = (a0+a1 > b0+b1)\n",
      "fig,ax=subplots()\n",
      "ax.plot(a1[idx],b1[idx],'o',alpha=.1)\n",
      "ax.plot(a0,b0,'rs',ms=15,alpha=.3)\n",
      "ax.plot(0,a0-b0,'r^',ms=15,alpha=.3)\n",
      "ax.plot(1-(a0-b0),1,'r^',ms=15,alpha=.3)\n",
      "ax.arrow(0,0,a0,b0,width=.002,length_includes_head=True)\n",
      "ax.arrow(a0,b0,0,a0-b0,width=.002,length_includes_head=True)\n",
      "ax.arrow(a0,b0,1+b0-a0,1,width=.002,length_includes_head=True,color='g')\n",
      "ax.arrow(0,0,1+b0-a0,1,width=.002,length_includes_head=True,color='g')\n",
      "ax.axis((0,1.2,0,1.2))\n",
      "ax.set_aspect(1)\n",
      "ax.set_xlabel('a',fontsize=18)\n",
      "ax.set_ylabel('b',fontsize=18)\n",
      "ax.plot(linspace(0,2,3),linspace(0,2,3),'k--',lw=3.)\n",
      "ax.set_title('prob = %3.3f,phat=%3.3f'%(1-(1-a0+b0)**2/2.,idx.mean()))\n",
      "ax.add_patch(Rectangle((0,0),1,1,alpha=.2,lw=2.,color='gray'))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 22,
       "text": [
        "<matplotlib.patches.Rectangle at 0x90ffbd0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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AUtc2Tatz2mkxXPcIpVKGj33sNUxMPAAoh+tNN72TJz7xDxkeDpNOhzEMAyld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ptdD9HPOvnXYlk26+tlisW6p1ZY4uKL9/X1PEuQSGSpVFQdlYpZCxynSjze72lt3FU83d1fzzec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\ng0hkfoAnpVooK7lW0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       "text": [
        "<matplotlib.figure.Figure at 0x8ef0f30>"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "b0,b1 = rand(2,1000)\n",
      "a0,a1 = rand(2,1000)\n",
      "mean((a0+b0) > (a1+b1))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "0.50800000000000001"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "idx = (a0>b0)\n",
      "mean(a0[idx]+a1[idx] > b0[idx]+b1[idx])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 45,
       "text": [
        "0.76771653543307083"
       ]
      }
     ],
     "prompt_number": 45
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.logical_and( a0>b0, (a0+a1) > (b0+b1)).mean() # 3/8 is exact solution"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "0.38"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.logical_and( a0>b0, (a0+a1) > (b0+b1)).mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "0.39400000000000002"
       ]
      }
     ],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "(a0>b0).mean()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 26,
       "text": [
        "0.52000000000000002"
       ]
      }
     ],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import sympy as S"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 47
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "a0,b0 = S.symbols('a0 b0')\n",
      "expr = S.integrate((1-(1-a0+b0)**2/2),(a0,b0,1))\n",
      "S.integrate(expr,(b0,0,1)) # prob of (a0>b0) AND (a0+a1>b0+b1)\n",
      "print 'conditional probability P(a0+a1>b0+b1|a0>b0) = %3.3f' % (float(_)/(0.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "conditional probability P(a0+a1>b0+b1|a0>b0) = 0.750\n"
       ]
      }
     ],
     "prompt_number": 52
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}